Self-Sustained Libration Regime in Nonlinear Microelectromechanical Devices

Abstract

We present a mode of operation for Duffing-type nonlinear microelectromechanical system devices whereby a self-sustained multifrequency output is generated. This self-sustained librator regime creates a limit cycle around a dynamical fixed point, i.e., around fixed points within the rotating frame, whereas a traditional oscillator generates a limit cycle around a static fixed point. The librator limit cycles thus created do not change the global topology of the rotating frame phase space, but are constrained by it. Because of the Duffing nonlinearity, different types of limit cycles could be generated within the same phase space, with each type possessing distinct dynamical features. Transitioning between these limit cycles requires crossing homoclinic bifurcations, which is done without generating chaos as the phase space dynamics are constrained in two dimensions. This work provides an alternative experimental tool for the study of microelectromechanical and nanoelectromechanical system dynamics and their application.